Just saying undulating twill brings a smile to my face. Flowing lines, curves, swaying objects are brought to mind.
In an undulating twill, pattern curves are created by having areas of tight interlacement followed by areas of more open weave in the same cloth. This is done by having areas of different size floats. The above weaving has reverses in the pattern causing the curves to reverse back. This creates the eyes.
The inconsistent interlacement may result in uneven wear. A different weave structure should be used if this is a concern. Network Twills have a more consistent interlacement and can give the appearance of curves in the fabric. One of my future projects will involve curves and Network Twills.